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▾
Bridge course
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Countable and uncountable sets
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Proof techniques
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Example of a nonconstructive proof
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Direct proof
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Disproof by counterexample
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Proof by cases
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Proving properties of absolute value
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Proof by contrapositive
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Proof by contradiction
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Proof by induction
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Proof by strong induction
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Proving de Moivre's theorem
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Visual proof
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Challenge
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Relations
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Equivalence relations
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Intersection of equivalence relations
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Representing relations using matrices
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Combining relations
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Composition of relations
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Inverse of composite relation
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Representing relations using digraphs
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Properties of relations
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Proving equivalence relations
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What is a relation?
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Finding the inverse of a relation on a finite set
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Functions (bridge course)
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Injective, surjective, and bijective
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Intro
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Is it bijective? (infinite domain)
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Is it injective?
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Is it surjective?
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Proof: Composite of surjections is surjection
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Proving properties of injective, surjective, and bijective functions
›
Bridge course
›
Functions (bridge course)
›
Injective, surjective, and bijective
Proving properties of injective, surjective, and bijective functions
The composition of injective functions is injective.
45458
The Composition of Injective(one-to-one) Functions is Injective Proof
The Math Sorcerer
If \(g \circ f\) is injective, then \(f\) is injective.
43934
Proof that if g o f is Injective(one-to-one) then f is Injective(one-to-one)
The Math Sorcerer
If \(g \circ f\) is surjective, then \(g\) is surjective.
46200
Proof that if g o f is Surjective(Onto) then g is Surjective(Onto)
The Math Sorcerer
45594
The Composition of Surjective(Onto) Functions is Surjective Proof
The Math Sorcerer
7927
Surjection if Composite is Surjection
ProofWiki
YouTube videos
45458
The Composition of Injective(one-to-one) Functions is Injective Proof
The Math Sorcerer